The importance of cosmological simulations as a tool to study the evolution
of our Universe has steadily grown over the recent years. Thanks to the
astonishing increase of computing power, numerical simulations have
accomplished tremendous progress, and are now able to recreate virtual
universes on a supercomputer that are in agreement with key observed
properties of galaxies. In my talk, I will review the challenges, both
physical and numerical, that cosmological simulations must overcome to
accomplish this feat. I will briefly describe how the fundamental physical
processes needed to model the formation and evolution of galaxies are
included in such codes, and present what is the state of the art in these
calculations. I will then review ongoing efforts aimed at improving the
maximum resolution, simulated volume and physical fidelity of the current
generation of cosmological simulations, an important step forward to build a
comprehensive theoretical understanding of the evolution of the Universe.